# CVP Relationships

05/05/2020

Cost Volume-Profit (CVP) relationship is an analysis which studies the relationships between the following factors and its impact on the amount of profits.

In simple words, CVP is a management accounting tool that expresses relationship among total sales, total cost and profit. Cost Volume-Profit relationship is one of the important techniques of cost and management accounting. It is a powerful tool which furnishes the complete picture of the profit structure and helps in planning of profits. It can also answer what if type of questions by telling the volume required to produce. This concept is relevant in all decision making areas, particularly in the short run.

Managerial accounting provides useful tools, such as cost-volume-profit relationships, to aid decision-making. Cost volume profit relationship helps you understand different ways to meet your company’s net income goals.

1. #### The Basics of Cost-Volume-Profit (CVP) Analysis

Cost-volume-profit (CVP) analysis is a key step in many decisions. CVP analysis involves specifying a model of the relations among the prices of products, the volume or level of activity, unit variable costs, total fixed costs, and the sales mix. This model is used to predict the impact on profits of changes in those parameters.

(a) Contribution Margin

Contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. It contributes towards covering fixed costs and then towards profit.

(b) Unit Contribution Margin

The unit contribution margin can be used to predict changes in total contribution margin as a result of changes in the unit sales of a product. To do this, the unit contribution margin is simply multiplied by the change in unit sales. Assuming no change in fixed costs, the change in total contribution margin falls directly to the bottom line as a change in profits.

(c) Contribution Margin Ratio

The contribution margin (CM) ratio is the ratio of the contribution margin to total sales. It shows how the contribution margin is affected by a given dollar change in total sales. The contribution margin ratio is often easier to work with than the unit contribution margin, particularly when a company has many products. This is because the contribution margin ratio is denominated in sales dollars, which is a convenient way to express activity in multi-product firms.

1. #### Some Applications of CVP Concepts

CVP analysis is typically used to estimate the impact on profits of changes in selling price, variable cost per unit, sales volume, and total fixed costs. CVP analysis can be used to estimate the effect on profit of a change in any one (or any combination) of these parameters. A variety of examples of applications of CVP are provided in the text.

1. #### CVP Relationships in Graphic Form

CVP graphs can be used to gain insight into the behavior of expenses and profits. The basic CVP graph is drawn with dollars on the vertical axis and unit sales on the horizontal axis. Total fixed expense is drawn first and then variable expense is added to the fixed expense to draw the total expense line. Finally, the total revenue line is drawn. The total profit (or loss) is the vertical difference between the total revenue and total expense lines. The break-even occurs at the point where the total revenue and total expenses lines cross.

1. #### Break-Even Analysis and Target Profit Analysis

Target profit analysis is concerned with estimating the level of sales required to attain a specified target profit. Break-even analysis is a special case of target profit analysis in which the target profit is zero.

(a) Basic CVP equations

Both the equation and contribution (formula) methods of break-even and target profit analysis are based on the contribution approach to the income statement. The format of this statement can be expressed in equation form as:

Profits = Sales – Variable expenses – Fixed expenses

(b) Break-even point using the equation method

The break-even point is the level of sales at which profit is zero. It can also be defined as the point where total sales equals total expenses or as the point where total contribution margin equals total fixed expenses. Break-even analysis can be approached either by the equation method or by the contribution margin method. The two methods are logically equivalent.

Margin of Safety

The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It is the amount by which sales can drop before losses begin to be incurred. The margin of safety can be computed in terms of dollars:

Margin of safety in dollars = Total sales – Break-even sales

Cost Structure

Cost structure refers to the relative proportion of fixed and variable costs in an organization. Understanding a company’s cost structure is important for decision-making as well as for analysis of performance.

Operating Leverage

Operating leverage is a measure of how sensitive net operating income is to a given percentage change in sales.

Assumptions in CVP Analysis

Simple CVP analysis relies on simplifying assumptions. However, if a manager knows that one of the assumptions is violated, the CVP analysis can often be easily modified to make it more realistic.

• Selling price is constant: The assumption is that the selling price of a product will not change as the unit volume changes. This is not wholly realistic since unit sales and the selling price are usually inversely related. In order to increase volume it is often necessary to drop the price. However, CVP analysis can easily accommodate more realistic assumptions. A number of examples and problems in the text show how to use CVP analysis to investigate situations in which prices are changed.
• Costs are linear and can be accurately divided into variable and fixed elements: It is assumed that the variable element is constant per unit and the fixed element is constant in total. This implies that operating conditions are stable. It also implies that the fixed costs are really fixed. When volume changes dramatically, this assumption becomes tenuous. Nevertheless, if the effects of a decision on fixed costs can be estimated, this can be explicitly taken into account in CVP analysis. A number of examples and problems in the text show how to use CVP analysis when fixed costs are affected.
• The sales mix is constant in multi-product companies: This assumption is invoked so as to use the simple break-even and target profit formulas in multi-product companies. If unit contribution margins are fairly uniform across products, violations of this assumption will not be important. However, if unit contribution margins differ a great deal, then changes in the sales mix can have a big impact on the overall contribution margin ratio and hence on the results of CVP analysis. If a manager can predict how the sales mix will change, then a more refined CVP analysis can be performed in which the individual contribution margins of products are computed.
• In manufacturing companies, inventories do not change: It is assumed that everything the company produces is sold in the same period. Violations of this assumption result in discrepancies between financial accounting net operating income and the profits calculated using the contribution approach. This topic is covered in detail in the chapter on variable costing.